IMHO, we're in an area of legal vs. moral here. One would presume that the street maintenance if not law enforcement authorities should/could have done something to (a) remove an apparently abandoned bike from a public area before it became essentially trash and and an eyesore, and (b) attempt to identify its owner and take the appropriate subsequent steps.
Yes, I'm with the cya peeps here, though I can't see how the owner has any residual rights at this point to the piece of junk that is now cluttering public property, by removing it of your own accord you still run a personal risk that is not commenssurate with the value of salvaging the bike from its likely fate. But that is my practical view, not my moral view. Morally, what you're contemplating is not that different from collecting aluminum soda cans from the roadside to recycle them (albeit for compensation), rather than leaving them to continue to spoil the view.